Relaxation of Chemical Reactions to Stationary States in the Chemical Affinities Space

TL;DR

This paper investigates how chemical systems relax to steady states in the chemical affinities space, revealing different behaviors inside and outside the Onsager region and deriving nonlinear closure equations.

Contribution

It introduces a geometric framework for chemical relaxation, deriving the affine connection and nonlinear closure equations near steady states, extending understanding beyond the Onsager region.

Findings

Relaxation follows a straight line in the Onsager region.

Out of the Onsager region, evolution aligns with the shortest path projections.

Derived the affine connection and nonlinear closure equations for thermodynamic forces.

Abstract

Using the mass balance equations for chemical reactions, we show how the system relaxes towards a steady state in and out of the Onsager region. In the chemical affinities space, after fast transients, the relaxation process is a straight line when operating in the Onsager region, while out of this regime, the evolution of the system is such that the projections of the evolution equations for the forces and the shortest path on the flows coincide. For spatially-extended systems, similar results are valid for the evolution of the thermodynamic mode (i.e., the mode with wave-number k = 0). These results allow us to obtain the expression for the affine connection of the space covered by the thermodynamic forces, close to the steady states. Through the affine connection, the nonlinear closure equations are derived.